Holistic Numerical Methods Institute

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Multiple Choice Test

Romberg Method of Integration

 

Q1. If  is the value of integral

  

using n-segment Trapezoidal rule, a better estimate of the integral can be found using Richardson’s extrapolation as

Q2. The estimate of an integral of

 

is given as 1860.9 using 1-segment Trapezoidal rule. 

 

Given f(7)=20.27, f(11)=45.125, and f(14)=82.23, the value of the integral using 2-segment Trapezoidal rule would most nearly be

787.32

1072.0

1144.9

1291.5

 

Q3. The value of an integral

 

given using 1, 2, and 4 segments Trapezoidal rule is given as 5.3460, 2.7708, and 1.7536, respectively.  The best estimate of the integral you can find using Romberg integration is most nearly

1.3355
 1.3813

1.4145
 1.9124

Q4. Without using the formula for one-segment Trapezoidal rule for

estimating the true error,  can be found directly as well as exactly by using the formula

 ,


Q5. For

,

the true error, in one-segment Trapezoidal rule is given by

 , . 

The value of for the integral  is most nearly

2.7998

4.8500

4.9601

5.0327

 

Q6. Given the velocity vs. time data for a body

 

t(s)

2

4

6

8

10

25

0.166

0.55115

1.8299

6.0755

20.172

8137.5

 

The best estimate for distance covered between 2s and 10s by using Romberg rule based on Trapezoidal rule results would be

33.456 m

36.877 m

37.251 m

81.350 m

 

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